A sum of Rs. 312 was divided among 100 boys and girls in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. Find the number of girls.

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The problem can be modeled using two linear equations: one for the total number of children and one for the total amount of money.
Let G be the number of girls and B be the number of boys. The equations are: B + G = 100 and 3.60B + 2.40G = 312.
Solving this system of equations yields G = 40.
Verification confirms the result: 60 boys at Rs. 3.60 each is Rs. 216, and 40 girls at Rs. 2.40 each is Rs. 96. The total is 216 + 96 = Rs. 312.

Option B: If there were 38 girls, there would be 62 boys. The total amount would be (62 × 3.60) + (38 × 2.40) = 223.20 + 91.20 = Rs. 314.40, which is not the given total of Rs. 312.
Option C: If there were 42 girls, there would be 58 boys. The total amount would be (58 × 3.60) + (42 × 2.40) = 208.80 + 100.80 = Rs. 309.60, which is not the given total of Rs. 312.
Option D: If there were 44 girls, there would be 56 boys. The total amount would be (56 × 3.60) + (44 × 2.40) = 201.60 + 105.60 = Rs. 307.20, which is not the given total of Rs. 312.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process of setting up the algebraic equations from the word problem and solving for the unknown variable.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a system of linear equations from a word problem as background academic context rather than a clinical decision trigger.
This question assesses basic mathematical and logical reasoning skills, which are foundational for various non-nursing components of competitive examinations.
While not directly related to clinical practice, strong analytical skills are essential for problem-solving in any professional field, including nursing.
What if? - If the stem changed one defining clue so that 40 no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, carefully read the problem to identify all the given quantities (total sum, total children, amount per boy, amount per girl) and what needs to be found (number of girls).
Define algebraic variables to represent the unknown quantities. For instance, let 'G' be the number of girls and 'B' be the number of boys.
Translate the word problem into a system of mathematical equations. You will need one equation for the total number of children and another for the total amount of money.
Solve the system of equations. A common method is substitution: solve one equation for one variable and substitute that expression into the other equation.
After finding the value of one variable (e.g., 'G'), calculate the other variable ('B').
Finally, check your answer by plugging the values back into the original problem statement to ensure they satisfy all conditions.

Concept Tested & Keywords

Concept Tested: Solving a system of linear equations from a word problem.
Stem keywords: sum of Rs. 312, 100 boys and girls, boy gets Rs. 3.60, girl Rs. 2.40
Lead-in keywords: Find the number of girls

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